Why can’t dividing by 0 be done in a theoretical field?

Question

As a layperson who is interested in math, imaginary numbers always fascinated me. Like in the real world you taking the square of a negative makes no sense whatso ever, but in theoretical math you can just invent new imaginary numbers, make it so that *i*^2 = -1 and suddenly you have just revolutionized math. If this is useful, why can’t you break other rules and account for them with new imaginary symbols?

So let’s pretend that we call them made up numbers and use *m* to represent them. Why is *m*=1/0 impossible when something like *i*^2 = -1 is not?

In: 27

Answer 1

You **can** divide by zero in some theoretical field. It just isn’t meaningful or helpful.

Imaginary numbers are just as real as other numbers. We use them to solve problems and make accurate predictions. If you’re trying to model what happens when you turn a crank, apply electricty to something, or run water through a wheel you’ll probably want to use imaginary numbers.

Imaginary numbers are all about change. It’s easy to say “I have one orange” and “You lost one orange” because we’re used to dealing with 1 and -1. But how many oranges do you have while you hand one to your friend? Do you both have 1? No, because there’s only one orange, not two. Do you both have half an orange? No, because the orange isn’t split in half. It’s more accurate to admit that the situation is complex. You can use imaginary numbers to model the gradual change of ownership during the handoff.

Let’s say you have a big group of people handing each other oranges. You can make an equation to calculate how many oranges each person has at any point in time. Using imaginary numbers will make this equation more accurate and meaningful. If you look really closely at one person during one moment you’re equation will show that he has some real oranges and some imaginary oranges. And that’s okay. At the end of the day, you wait until all the handoffs are complete before telling everyone to stop and go home.

Even when you’re working with imaginary numbers you usually do the math so that those imaginary numbers are elminated from the final result. You don’t want to leave things partway complete; you want things to settle down into something more tangible.